We examined biases in the global GEOS-Chem chemical transport model for the period of February–May 2010 using weak-constraint (WC) four-dimensional variational (4D-Var) data assimilation and dry-air mole fractions of CH4 (XCH4) from the Greenhouse gases Observing SATellite (GOSAT). The ability of the observations and the WC 4D-Var method to mitigate model errors in CH4 concentrations was first investigated in a set of observing system simulation experiments (OSSEs). We then assimilated the GOSAT XCH4 retrievals and found that they were capable of providing information on the vertical structure of model errors and of removing a significant portion of biases in the modeled CH4 state. In the WC 4D-Var assimilation, corrections were added to the modeled CH4 state at each model time step to account for model errors and improve the model fit to the assimilated observations. Compared to the conventional strong-constraint (SC) 4D-Var assimilation, the WC method was able to significantly improve the model fit to independent observations. Examination of the WC state corrections suggested that a significant source of model errors was associated with discrepancies in the model CH4 in the stratosphere. The WC state corrections also suggested that the model vertical transport in the troposphere at middle and high latitudes is too weak. The problem was traced back to biases in the uplift of CH4 over the source regions in eastern China and North America. In the tropics, the WC assimilation pointed to the possibility of biased CH4 outflow from the African continent to the Atlantic in the mid-troposphere. The WC assimilation in this region would greatly benefit from glint observations over the ocean to provide additional constraints on the vertical structure of the model errors in the tropics. We also compared the WC assimilation at 4∘ × 5∘ and 2∘ × 2.5∘ horizontal resolutions and found that the WC corrections to mitigate the model errors were significantly larger at 4∘ × 5∘ than at 2∘ × 2.5∘ resolution, indicating the presence of resolution-dependent model errors. Our results illustrate the potential utility of the WC 4D-Var approach for characterizing model errors. However, a major limitation of this approach is the need to better characterize the specified model error covariance in the assimilation scheme.